NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Francois Tremblay
Date: 2022 Jun 26, 10:43 -0700
Hello all,
I am relatively new to celestial navigation but very much deep into it. As an engineer, I make a point in making sure that all my calculations are precise. So far everything has worked out very nicely. But I’m now challenged by a mathematical error that I can’t figure out. It might just be the precision of the tables versus mathematical calculation. I would appreciate your input on it.
Here’s the problem.
I want to get the azimuth of the sun at sunrise at a specific position in the Northern Atlantic to verify the error of my compass.
Date: June 16^{th}, 2022
My position: N 48° 17.0’ W 062° 28.0’.
At this position, the sun will rise at exactly 8h08 TU (3h58 + 4)
N 50° | 03 50 |
N 48° 17.5 | 03 58 |
N 45° | 04 13 |
Option 1. Using HO-249 the same way I do for any other sightings.
I enter the table with DEC N 23° 23.0 / Latitude N 48° / LHA 239°. The azimuth is 052°, which makes sense.
Option 2. Using Bowditch Tables
I enter the table with DEC 23° and Latitude 48°. The azimuth is 054.3°. It also makes sense.
Option 3. Finally, I use the amplitude formula instead of the Bowditch table
A°= arcsin (sin DEC / cos a-Lat)
A°= arcsin (sin 23° 23.0’ / cos 48° 17’)
A°= arcsin (sin 23.383° / cos 48.283°)
A°= 36.6°
Z = 090 – 36.6° = 53.4°
Here’s my question: The three results make sense but are slightly different (052°, 054.3° and 053.4°). Is it only due to the precision of the tables or is there something I forget to consider. Also, when using the first method, while the azimut (052°) seems to make sense, I get a Hc of -1° 15’. It seems to me that Hc should be very close to 0°
Thanks for your input!
Francois